---
title: "Sampling, holding, quantizing, coding and decoding"
subject: "Digital Control System"
chapter: 1
key: "semester_6/digital_control_system:sampling-quantizing-coding-terms"
source: https://www.bctengineer.com/q/semester_6/digital_control_system/sampling-quantizing-coding-terms
site: BCT Engineering
---

# Sampling, holding, quantizing, coding and decoding

Digital Control System · Chapter 1: Introduction to Discrete Time Control System

- Asked in: 2082 Kartik, 6 marks
- Video: [Quantization (Basics, Working Principle, Waveforms, Quantization Error & Quantization Noise)](https://www.youtube.com/watch?v=cUdnGkymAWU) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/digital_control_system/sampling-quantizing-coding-terms
- Whole chapter: https://www.bctengineer.com/md/semester_6/digital_control_system/chapter-1

## Question

Define the term sampling, holding, quantizing, coding and decoding used in analog to digital converter. Also mention the advantages of digital control system over analog control system.

## Short answer

Sampling takes signal values at discrete instants; holding keeps them constant; quantizing rounds to finite levels with step Q=FSR/2^n; coding assigns binary words; decoding converts back to analog. Advantages: flexible, accurate, noise-immune, supports complex control, multi-loop sharing, easy storage and networking.

## Answer

An analog-to-digital converter changes a continuous signal into binary numbers in several steps, and a decoder (D/A) changes them back.

```text
 x(t) -> Sampler -> Hold -> Quantizer -> Encoder -> binary
                                                    word
```

#### Terms

- **Sampling:** taking the value of the continuous signal only at discrete instants $t = kT$ ($T$ = sampling period). The output is a discrete-time signal $x(kT)$ of continuous amplitude.
- **Holding:** keeping the sampled value constant for the conversion time (or until the next sample) by a sample-and-hold or zero order hold circuit, so the converter sees a steady input.
- **Quantizing:** rounding (or truncating) the held amplitude to the nearest of a finite set of levels. For an n-bit ADC with full-scale range $FSR$, there are $2^n$ levels and the step size is $Q = FSR/2^n$. The difference between true and quantized value is the quantization error, at most $\pm Q/2$.
- **Coding (encoding):** assigning a binary code (straight binary, BCD, two's complement, Gray) to each quantized level, giving an n-bit word. Example: 3-bit ADC, $FSR = 8$ V, input 5.3 V is quantized to level 5, coded as 101.
- **Decoding:** the reverse process in a D/A converter: converting the binary word back into an analog voltage, $V = Q \times (\text{decimal value of code})$. With a hold circuit this gives a staircase signal.

#### Advantages of digital control system over analog

- **Flexible:** control law changed by reprogramming, not rewiring.
- **Accurate and drift-free:** no change with temperature or ageing of components.
- **Better noise immunity** of digital signals.
- **Complex/adaptive/nonlinear control** is easy to implement in software.
- **One computer serves many loops** (time sharing), so cost per loop is low.
- **Easy data storage, display, alarms and networking.**
- **Smaller, cheaper, more reliable** hardware.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For an n-bit ADC with full-scale range FSR, what is the step size Q and the maximum quantization error?
   A. Q = FSR/2^n, error at most ±Q/2
   B. Q = FSR*2^n, error at most ±Q
   C. Q = FSR/n, error at most ±2Q
   D. Q = 2^n/FSR, error zero
   Answer: A. There are 2^n levels so Q = FSR/2^n, and rounding gives an error of at most ±Q/2. (Key point: Quantization step)

2. A 3-bit ADC with FSR = 8 V receives 5.3 V. What is the quantized level and code?
   A. Level 4, 100
   B. Level 5, 101
   C. Level 6, 110
   D. Level 5, 110
   Answer: B. Q = 8/8 = 1 V, so 5.3 V rounds to level 5, coded 101. (Key point: Coding example)

3. What does sampling produce?
   A. A signal with discrete amplitude but continuous time
   B. A discrete-time signal x(kT) of continuous amplitude
   C. A binary word
   D. A staircase analog signal
   Answer: B. Sampling takes values at discrete instants t = kT, keeping the amplitude continuous. (Key point: Sampling definition)

4. What is decoding in this chain?
   A. Rounding to the nearest level
   B. Reverse process in a D/A converter: V = Q x (decimal value of code)
   C. Assigning binary codes
   D. Holding the sample
   Answer: B. Decoding converts the binary word back into an analog voltage. (Key point: Decoding)

## Related in Digital Control System

- [Advantages of digital over analog control](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adcs-advantages-over-analog) — Digital Control System, chapter 1, asked 3×
- [Digital control system block diagram and advantages](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adcs-block-diagram-advantages) — Digital Control System, chapter 1, asked 3×
- [Types of signals in digital control](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Asignal-types-in-dcs) — Digital Control System, chapter 1
- [Digital control system and function of each block](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adcs-function-of-each-block) — Digital Control System, chapter 1, asked 4×
- [Short note: Digital to analog conversion](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Ashort-note-dac) — Digital Control System, chapter 1
- [Sampling operations and DCS advantages](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Asampling-operations-advantages) — Digital Control System, chapter 1

## Related in other subjects

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